{"paper":{"title":"4-Regular oriented graphs with optimum skew energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Huishu Lian, Xiaolin Chen, Xueliang Li","submitted_at":"2013-04-03T06:00:28Z","abstract_excerpt":"Let $G$ be a simple undirected graph, and $G^\\sigma$ be an oriented graph of $G$ with the orientation $\\sigma$ and skew-adjacency matrix $S(G^\\sigma)$. The skew energy of the oriented graph $G^\\sigma$, denoted by $\\mathcal{E}_S(G^\\sigma)$, is defined as the sum of the absolute values of all the eigenvalues of $S(G^\\sigma)$. In this paper, we characterize the underlying graphs of all 4-regular oriented graphs with optimum skew energy and give orientations of these underlying graphs such that the skew energy of the resultant oriented graphs indeed attain optimum. It should be pointed out that th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0847","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}